This Selected Issues paper estimates an equilibrium path for South Africa’s real effective exchange rate. The paper briefly describes the dynamics of the real exchange rate and its determinants. It investigates the presence of a long-term relationship between the real exchange rate and certain explanatory variables, estimates the speed at which the real exchange rate converges toward its equilibrium level, and derives measures for the equilibrium real exchange rate. The paper also examines the real money demand, consumer prices, and the real exchange rate in South Africa.

Abstract

This Selected Issues paper estimates an equilibrium path for South Africa’s real effective exchange rate. The paper briefly describes the dynamics of the real exchange rate and its determinants. It investigates the presence of a long-term relationship between the real exchange rate and certain explanatory variables, estimates the speed at which the real exchange rate converges toward its equilibrium level, and derives measures for the equilibrium real exchange rate. The paper also examines the real money demand, consumer prices, and the real exchange rate in South Africa.

II. Real Money Demand, Consumer Prices, and the Real Exchange Rate in South Africa16

A. Introduction

24. In February 2000, South Africa adopted an explicit inflation-targeting strategy for monetary policy. The CPIX17 inflation target was set at 3–6 percent (annual average) in 2002 and 2003, and then at 3–5 percent in 2004 and 2005. This change in policy regime comes after a period of disinflation in the 1990s when annual inflation fell from 18 percent in 1991 to 7 percent in 1998. Over the same period there were large fluctuations in money growth and the exchange rate. This section analyzes the relationship between money, prices, and the exchange rate in South Africa using an economic model which incorporates three relationships - money demand, a markup model of the level of CPLX, and the real exchange rate - that together provide an analytical framework for examining the forces that explain the historical fluctuations in the money supply, the real exchange rate, and the level of CPIX.

25. A number of policy issues are discussed as part of the analysis including whether there continues to be a stable relationship between money and prices, so that, potentially, this information can be used to assess the prospects for CPIX inflation. This section also tests whether cost-push factors help to explain CPLX inflation in South Africa. A stable long-run relationship would suggest that policymakers should take into account unit labor costs and production prices when assessing the prospects for CPLX inflation. This section also tests for a real exchange rate relationship so that the role of foreign shocks, which should play an important role in an open economy such as South Africa, is incorporated into the model.

26. This analysis begins by testing whether there exist stable, long-run (cointegrating) relationships for money demand, the real exchange rate and a markup model of CPLX using the Johansen (1988) cointegrating vector autoregression (CVAR) methodology; it then examines the short-run deviation of real money balances, the level of CPLX, and the real exchange rate from their long-run paths given by the cointegrating vectors (see Table II. 1 for the cointegrating vectors).18 An analysis of the short-run deviations reveals that significant excess money balances were building from late 1998, and were associated with an undervalued real exchange rate (relative to its long-run value) and a level of CPIX that was higher than suggested by total unit costs of production. Finally, impulse response functions are examined for three different shocks to assess the model’s dynamic properties.

Table II. 1.

Long-run economic relationships26

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27. The rest of the section is structured as follows: subsection B discusses money demand, the real exchange rate, and the markup model, including a brief survey of some earlier literature; subsection C discusses the methodology, the data and the main results; and subsection D concludes.

B. Background and Theory

28. This section builds on previous work in a number of ways.19 First, the analysis extends into the latest available data, which include the period of considerable financial market volatility seen in emerging markets during the Asian financial crisis. This allows a test of whether this period of volatility, especially in the rand exchange rate, led to instability in the estimated long-run relationships, or whether the impact was temporary, resulting in short-run (temporary) deviations of real money balances, prices and the real exchange rate from their long-run path. Second, this section tests whether the markup model explains the level of CPIX and third, it uses the CPIX as its measure of consumer prices, because the inflation target in South Africa is expressed in terms of CPIX inflation.

29. The theory underpinning each of the three long-run structural relationships is briefly discussed below:

Long-run money demand

30. The building blocks of money demand theory suggest that the demand for real money balances are a function of a scale variable (y in equation 1) that captures the transactions demand (e.g. real GDP) and the opportunity cost of holding money captured by an appropriate interest rate, R:

MP=αy+βrOWN+λR(1).

31. In the empirical literature a number of refinements have been made to the basic model when using a broad measure of money, such as M3, to include a variable that captures the own rate of return, rown, on those elements that are interest bearing.20 Because data on the bank deposit rate is available only since 1980, the three-month treasury bill rate is used as a proxy for the own rate of return, rown, because the two interest rates are highly correlated.21

32. Recent studies of money demand in South Africa (see DeJaeger and Ehlers (1997); Jonsson (2001); and Hurn et al. (1992), find that broad money (M3) rather than narrow money has a stable relationship with prices and is a better leading indicator of inflation.

Long run real exchange rate and purchasing power parity (PPP)

33. The PPP model suggests the following relationship (all variables in logarithms):

PP*=ηe(2)

where Px is the foreign price level, e is the nominal exchange rate (measured as the nominal effective exchange rate), and P is the domestic price level (CPIX). A coefficient of unity on the exchange rate22 captures the idea of PPP because it means the exchange rate moves to exactly offset a shock to domestic prices, thereby returning the real exchange back to its PPP level. Most empirical work on the real exchange rate fails to find support for PPP across a variety of countries, using different econometric techniques and sample periods (see Rogoff, 1996). However, support for relative PPP is easier to find in the literature; namely, that changes in the exchange rate are determined in the long run by relative inflation rates. One explanation for the incomplete exchange rate pass-through to the general level of prices might be that a large proportion of goods and services included in consumer price indices are typically nontraded.23

Markup Model

34. If we assume long-run homogeneity24 between CPIX (P), unit labor costs (ULC), and producer prices (Pin), the markup model of inflation suggests the following relationship where γ+κ=125:

P=μ(ULC)γ(Pln)k(3)

35. This relationship states that, in the long run, the general level of prices is a stable markup over total unit costs. Fedderke and Schaling (2001) find evidence for a markup relationship linking output prices (measured using the GDP deflator) to total costs in South Africa with the average markup approximately three times that in the United States.

C. Methodology and Results

36. The cointegrating VAR comprised nine variables, and the Johansen trace test suggested there were four cointegrating vectors (the long-run relationships). Using appropriate restrictions on the cointegrating space, it was possible to identify the following long-run relationships (Table II.1.).

37. A number of inferences can be made from the table.27 The finding of a stable long-run real money demand relationship supports the hypothesis that money and prices move together in the long-run in South Africa.28 All the variables have the correct signs in the real money demand equation (model 1), and the income elasticity with respect to real money balances is0.55, suggesting that, in the long run, there are economies to scale to holding real money balances for transactions purposes. Both the own rate of interest, rown, (three-month treasury bill rate) and R, enter the real money demand equation with the expected signs, indicating that the demand for interest-bearing components of M3 increases with the return on short-term bonds, while the opportunity cost of money rises as the return on longer-term bonds increases.

38. Model 2 is a stable long-run relationship between the price level (CPIX) and total unit costs. Moreover, the restriction of static linear homogeneity was accepted (λ+κ=1 in model 2), indicating that prices in the long run increase in proportion with total unit costs.

39. Model 3 is a stable real exchange rate relationship. However, the restriction of purchasing power parity (PPP) is not accepted by the data, a finding similar to numerous other studies that test for PPP, and is consistent with the fact that the long-run real exchange rate has been on a depreciating trend over the sample period studied in this paper.

Testing the stability of the estimated long-run economic relationships

40. The literature on the empirical modeling of money demand generally finds that periods of structural change caused, for example, by financial liberalization have rendered money demand unstable across a wide range of countries (see Ericsson, 1998 and Sriram, 2000, for a survey).

41. Recursive estimates suggest the parameters are stable across all three estimated long-run cointegrating relationships, even at a statistical confidence level of I percent.29 The recursive estimates of the money demand parameters are stable in the latter part of the 1990s and into 2001 (Figure II.1).

Figure II. 1.
Figure II. 1.

Recursive Estimates of the Real Money Demand Parameters

Citation: IMF Staff Country Reports 2003, 018; 10.5089/9781451840995.002.A002

Figure II.2.
Figure II.2.

Recursive Estimates for the Real Exchange Rate Parameters

Citation: IMF Staff Country Reports 2003, 018; 10.5089/9781451840995.002.A002

42. The long-run real exchange rate parameters seem stable since 1994, including around the time of the Asian crisis, when the rand was under pressure, indicating that there was no impact on the long-run path of the real exchange rate.

Figure II.3.
Figure II.3.

Recursive Estimates of the Parameters in the Markup Relationship

Citation: IMF Staff Country Reports 2003, 018; 10.5089/9781451840995.002.A002

43. Recursive estimates of the markup parameters are also stable, suggesting that, in aggregate, the long-run markup over unit costs has been stable.

Deviations from the long-run path

44. At any point in time, real money balances, CPIX, and the real exchange may deviate from their respective long-run paths, but the vector error-correction mechanism (VECM), which govern the dynamics of the model, ensures that these deviations are temporary30. Towards the end of the sample, real money balances were approximately 30 percent higher than their estimated long-run value, suggesting the presence of “excess money” in the economy (Figure II.4). At the same time, the real exchange rate was approximately 25 percent below its long-run value (Figure II.5)31, and the level of CPIX was about 3 percent above its long-run level consistent with the level of total unit costs (Figure II.6).

Figure II.4.
Figure II.4.

Percent Deviation in Real Money Balances from Long-Run Path

Citation: IMF Staff Country Reports 2003, 018; 10.5089/9781451840995.002.A002

Figure II.5.
Figure II.5.

Percent Deviation of the Real Exchange Rate from its Long-Run Path

Citation: IMF Staff Country Reports 2003, 018; 10.5089/9781451840995.002.A002

Figure II.6.
Figure II.6.

Percent Deviations from Long-run Price Level: The Cost-Push Model

Citation: IMF Staff Country Reports 2003, 018; 10.5089/9781451840995.002.A002

45. The model cannot be used to draw a causal link between excess money balances, on the one hand, and an undervalued real exchange rate on the other hand, but because the three long-run relationships are identified within the same model, they are jointly determined in a general equilibrium framework. Moreover, over this period, excess real money balances and an under-valued real exchange rate were associated with CPIX above its long-run value. Therefore, when taken together, a plausible interpretation would be that excess money was putting pressure on the exchange rate and, together, they resulted in upward pressure on the price level.

The Impulse Response Analysis

46. The impulse response analysis provides information about the dynamic properties of the VECM and serves two purposes. First, it complements the previous discussion by revealing how variables respond to economic shocks that may, in the first instance, cause them to deviate from their long-run path. Second, it is another check on the model’s economic interpretability. In the following analysis, three shocks are considered (each is one standard error in size): a shock to real money balances, a shock to the nominal effective exchange rate, and a shock to unit labor costs. Each impulse response has an interpretation consistent with economic theory.

47. While a shock to real money balances can originate from a number of sources, based on the dynamic responses of the other variables, the shock in Figure II.7 should be interpreted as an exogenous increase in the demand for real money balances.32 In response to this shock, short-term interest rates rise, reflecting a tightening of monetary conditions (the liquidity effect), and, via the expectations theory of the term structure of interest rates, there is a smaller increase in long-term rates, R - the yield curve inverts. The response of output is statistically insignificant over the impulse response period and is not included in Figure II. 7.

Figure II.7.
Figure II.7.

Impulse Response Analysis in the Monetary System: A Shock to Money Balances

Citation: IMF Staff Country Reports 2003, 018; 10.5089/9781451840995.002.A002

48. An increase in the nominal effective exchange rate, e, (an appreciation) results in a permanently lower level of CPIX, which adjusts to its new long-run level only gradually (Figure II.8).

Figure II.8.
Figure II.8.

The Real Exchange Rate Impulse Response: A Shock to the Nominal Effective Exchange Rate

Citation: IMF Staff Country Reports 2003, 018; 10.5089/9781451840995.002.A002

The level of CPIX increases in response to a positive shock to unit labor costs. Producer prices increase in the short-run, but then settle to their initial value in the long run (Figure II.9). The rise in unit labor costs is matched by the rise in CPIX, which is consistent with the finding of long-run static homogeneity between total unit costs and CPIX.

Figure II.9.
Figure II.9.

The Response of CPIX to a Shock to Unit Labor Costs

Citation: IMF Staff Country Reports 2003, 018; 10.5089/9781451840995.002.A002

D. Conclusion

49. This section finds support for a stable long-run real money demand relationship, a stable long-run relationship between total unit cost and the level of CPIX, and a stable long-run real exchange rate relationship. Real money balances, CPIX and the real exchange rate do not appear to have deviated significantly from their respective long-run paths over the period of the Asian financial crisis. However, toward the latter part of the sample, there is evidence of significant excess real money balances, combined with a substantial undervaluation of the real exchange rate (relative to its long-run value); meanwhile the level of CPIX is a little above the level predicted by the long-run markup relationship.

50. From a policy perspective, the results indicate that real money balances continue to be important for understanding long-run developments in the money market in South Africa and that money should be incorporated into any analysis of the prospects for CPIX inflation. The results also show that cost-push factors have played an important role in the determination of CPIX, and that, on average, shocks to the nominal exchange rate have tended to result in a permanent change in the level of the real exchange rate, and an improvement in external competitiveness.

References

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  • DeJaeger, C. and Ehlers, R. (1997), “The Relationship Between South African Monetary Aggregates, Interest Rates, and Inflation - A Statistical Investigation,unpublished Johannesburg: South African Reserve Bank, Economics Department.

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  • Ericsson, Neil (1998), “Empirical Modeling of Money Demand,Empirical Economics, Vol. 23, pp. 295315.

  • Fedderke, J. and Schaling, E. (2001) “Modelling Inflation In South Africa: A Multivariate Cointegration Analysis,Rand Afrikaans University, Research Paper No. 10

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  • Froot, Kenneth, Kim, Michael, and Rogoff, Kenneth (1995), “The Law of One Price Over 700 Years,NBER Working Paper No. 5312

  • Hurn, A. and Muscatelli, V. (1992), “The Long-Run Properties of the Demand for M3 in South Africa,South African Journal of Economics, Vol. 60, No. 2, pp. 15972

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  • Johansen, Soren (1988), “Statistical Analysis of Cointegrating Vectors,Journal of Economic Dynamics and Control, Vol. 12, No. 2/3, pp. 23154

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  • Jonsson, Gunnar (2001), “Inflation, Money Demand, and Purchasing Power Parity in South Africa,IMF Staff Papers, Vol. 48, number 2, pp. 24365

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  • Rogoff, Kenneth (1996), “The Purchasing Power Parity Puzzle,Journal of Economic Literature, Vol. 34, No. 2, pp. 64768

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APPENDIX: The VECM Estimates

The variables correspond to the following names listed in the results table:

CointEql to CointEq3 are the real money demand cointegrating equation, the real exchange rate cointegrating equation, and the markup cointegrating equation, respectively. CointEq4 is unrestricted and has no economic interpretation.

LM3-log of M3

LGDP- log of real GDP

LCPIX-log of CPIX

TREASURY-level of three-month treasury bill interest rate, rown.

BOND - 10-year bond yield, or the opportunity cost variable, R.

LULC - log of unit labor costs

LPRODDP - log of production price index

LPCPIN - log of trade-weighted foreign price level.

LOGE - log of the nominal effective exchange rate.

D - this prefix indicates the first difference of a variable.

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16

Prepared by Ashok Bhundia.

17

CPIX is the consumer price index, excluding interest on mortgage bonds.

18

If a set of (nonstationary) variables are cointegrated, then there exists an equivalent error-correction representation that characterizes the tendency of the system to converge to its long-run path.

19

See Jonsson (2001), and DeJaeger and Ehlers (1997) for previous studies which focus on some of the issues discussed in this section.

20

See Sriram (2000) for a survey.

21

The correlation between the bank deposit rate and the 3-month treasury bill is0.91 for the period 1980–2000.

22

In the analysis below, the exchange rate is defined such that an increase in the nominal exchange rate is an appreciation, so that we would expect a coefficient of negative 1 if PPP holds.

23

Bhundia (see section III of the selected issues paper) and Choudhri and Hakura (2001) find only partial pass-through to consumer prices for South Africa.

24

In this context, homogeneity assumes a constant markup over total unit costs in the long-run so that the level of CPIX increases (decreases) by the same proportion as the increase (decrease) in total unit costs.

25

γ and κ are elasticities that relate CPIX to unit labor costs and producer prices, respectively.

26

A time dummy from 1994Q1 to 2001Q2 was included as an unrestricted variable to capture the change in regime in 1994 following the end of apartheid,

27

Identification of the long-run relationships in the cointegrating VAR requires the imposition of restrictions on the estimated cointegrating vectors, and therefore t-statistics are not available for the restricted coefficients. However, the four overidentifying restrictions imposed on the cointegrating space were accepted −X2 (4) = 14.82 (0.06 probability).

28

Jonsson (2001) also finds evidence for a stable demand for real money balances (using M3).

29

In the early part of a recursive estimation exercise, the estimated parameters are more likely to appear unstable when the data sample is short and there are low degrees of freedom. However, the degrees of freedom constraint eases with each successive recursive estimate, and so the absence of a shift in the latter part of the sample period suggests the estimated parameters are stable.

30

The VECM estimates are reported in the appendix.

31

The long-run real exchange rate path is not the same as an equilibrium real exchange rate concept that is modeled and reported in section I because it is not based on judgements about the long-run sustainable path of macroeconomic variables that determine the real exchange rate, consistent with internal and external macroeconomic equilibrium. Consequently, the short-run deviations reported here cannot be compared to the over/undervaluation profile for the real exchange reported in section I of the chapter.

32

Money is demand determined in South Africa as the SARB (South African Reserve Bank) sets a policy interest rate and not the supply of money.

South Africa: Selected Issues
Author: International Monetary Fund
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    Recursive Estimates of the Real Money Demand Parameters

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    Recursive Estimates for the Real Exchange Rate Parameters

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    Recursive Estimates of the Parameters in the Markup Relationship

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    Percent Deviation in Real Money Balances from Long-Run Path

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    Percent Deviation of the Real Exchange Rate from its Long-Run Path

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    Percent Deviations from Long-run Price Level: The Cost-Push Model

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    Impulse Response Analysis in the Monetary System: A Shock to Money Balances

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    The Real Exchange Rate Impulse Response: A Shock to the Nominal Effective Exchange Rate

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    The Response of CPIX to a Shock to Unit Labor Costs